A conservative adaptive rank method for the Wigner-Poisson system

Mathematics > Numerical Analysis [Submitted on 18 Jun 2026] Title:A conservative adaptive rank method for the Wigner-Poisson system View PDF HTML (experimental)Abstract:We propose a conservative adaptive rank method for the 1D1V Wigner-Poisson system. The method targets a central challenge in deterministic quantum kinetic simulations: reducing the cost of phase-space evolution while preserving the macroscopic invariants needed for physical fidelity. The scheme combines a sampling-based adaptive rank Wigner-Poisson update [7] with a conservative macroscopic correction. A conservative density-momentum solve provides local macroscopic updates, a Fermi-Dirac-type reconstruction transfers them to the kinetic solution, and a global quadratic moment correction enforces the discrete total energy constraint at the kinetic level. Unlike Maxwell-Boltzmann-type corrections commonly used in classical kinetic settings, the reconstruction uses a Fermi-Dirac-type form motivated by the model's quantum-statistical structure. The corrected state is incorporated into an ACA SVD representation, allowing the numerical rank to adapt to the phase-space complexity generated by the nonlocal Wigner operator and self-consistent Poisson field. Numerical experiments for the two-stream instability, strong Landau damping, and bump-on tail instability show that the method captures benchmark Wigner-Poisson dynamics for several values of the quantum parameter H, maintains bounded adaptive ranks, and preserves the specified global discrete invariants with conservation errors near machine precision. We also compare this formulation, which uses local density-momentum correction plus global total energy correction, with a related globally conservative formulation for mass, momentum, and energy [8]. The two approaches produce nearly identical phase-space and diagnostic results for the periodic benchmark test considered here, indicating that both correction strategies are compatible with adaptive rank compression for Wigner-Poisson dynamics in the tested 1D1V periodic setting. Submission history From: Francisco Alejandro Padilla Gomez [view email][v1] Thu, 18 Jun 2026 13:47:04 UTC (8,152 KB) Current browse context: math.NA References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer (What is the Explorer?) Connected Papers (What is Connected Papers?) Litmaps (What is Litmaps?) scite Smart Citations (What are Smart Citations?) Code, Data and Media Associated with this Article alphaXiv (What is alphaXiv?) CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub (What is DagsHub?) Gotit.pub (What is GotitPub?) Hugging Face (What is Huggingface?) ScienceCast (What is ScienceCast?) Demos Recommenders and Search Tools Influence Flower (What are Influence Flowers?) CORE Recommender (What is CORE?) arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.